philosophy discussion 3
Valerielee
ExplainingtheLiarParadox.pdf
3/9/2018
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Phil 2: Puzzles and Paradoxes
Prof. Sven Bernecker
University of California, Irvine
Explaining the
Liar Paradox
• The liar paradox is attributed to the Greek
philosopher Epimenides (6th century BC), a Cretan,
who reportedly stated that "All Cretans are liars.“
• One version of the liar paradox is attributed to the
Greek philosopher Eubulides of Miletus (4th century
BC). Eubulides reportedly asked, "A man says that he
is lying. Is what he says true or false?“
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History of the Liar Paradox
• The Indian grammarian-philosopher Bhartrhari
(late 5th century CE) was well aware of a liar
paradox which he formulated as "everything I am
saying is false.”
• The Persian scientist Naṣīr al-Dīn al-Ṭūsī (1201-
1274) could have been the first to identify the liar
paradox as self-referential.
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Indexicals
• Indexicals are words whose referent and meaning are
determined by such contextual factors as the time, location, and
intentions of the speaker. Examples:
• Pronouns: I, he, she, this, that
• Adverbs: here, now, actually, presently, today, yesterday, tomorrow
• Adjectives: my, his, her, actual, past, present, future, left/right, up/down
• See lecture “A-Theory and B-Theory of Time,” slide #5
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Self-Referential Sentences
• A self-referential sentences is a sentences that refers to
themselves as a sentence.
• Examples:
– John is reading this sentence
– This sentence contains exactly threee erors.
– “Ice” has three letters
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Self-contradictory statements (cf. Harold Evans, Newsman's English, 1972,
p. 182)
• Make each pronoun agree with their antecedent.
• Join clauses good, like a conjunction should.
• Verbs has to agree with their subjects.
• Don't write run-on sentences they are hard to read.
• Don't use commas, which aren't necessary.
• It's important to use your apostrophe's correctly.
• Proofread your writing to see if you any words out.
• The passive voice is to be avoided.
• Try to not ever split infinitives.
• Don't use no double negative.
• Correct spelling is esential.
• Don't abbrev.
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Liar Paradox
• Suppose L1 is true; then it is as it says it is – false. So L1 is false.
However, suppose that it is false. Well, false is just what it says it is,
and a sentence that tells it the way it is is true. So L1 is true. So, if L1 is true, it is false; and if it is false, it is true. So it seems that L1 is
neither true nor false.
• This is a paradox if we assume the principle of bivalence. This
principle states that declarative sentences such as L1 are either true
or false.
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This sentence is false L1: L1 is false
Principle of Bivalence
• Principle of Bivalence: Every declarative statement has exactly
one truth value, either true or false.
• Motivation: “any non-defective representation of how things are
in the world must be either accurate or inaccurate, true or false”
(Sainsbury, p. 113).
• Are there counterexamples to the principle of bivalence (not
counting aesthetic, theological and ethical judgments)?
– You have stopped beating your wife
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Analysis of the Liar Paradox
By the principle of bivalence, L1 is either true or false.
First, let‘s assume the L1 is true.
1) “L1” is true Assumption
2) L1 (1), Disquotation
C) “L1” is not true (2), Def of L1
• (1) & (C) form a contradiction
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L1: L1 is false
Next, let‘s assume L1 is false.
1) “L1” is not true Assumption
2) L1 (1), Def of L1
C) “L1” is true (2), Disquotation
• (1) & (C) form a contradiction
• Thus we can derive a contradiction from the assumption that “‘L1’
is true or ‘L1’ is not true.” So we have a violation of the principle
of bivalence.
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Strengthened Liar
• Suppose we claim that L1 is neither true nor false. Let’s call this
claim G.
• G entails that L1 is not false. But if L1 is not false, then not-L1 is
true. And if not-L1 is true, then L1 is false. So G entails a
contradiction: L1 is not false and L1 is false.
• So we cannot solve the liar paradox by claiming that L1 is neither
true nor false.
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G: L1 is neither true nor false.
A tongue-in-cheek liar-style puzzle:
A: This sentence contains seven words.
• Sentence A is clearly false. So its opposite ought to be true.
Right?
B: This sentence does not contain seven words.
• Sentence B is the opposite of A and it is false too. How could
this be?
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